What does it mean when some book says that some algorithm is not so obvious, and then in brackets () says that this is possibly “the biggest understatement in this book”? Is the writer actually contradicting himself? If understatement means “state weakly” then is this the proper usage?

This is the actual sentence:

Strassen’s algorithm is not at all obvious. (This might be the biggest understatement in this book.)

4 Answers
4

What the author is saying in this case is that Strassen's algorithm is very, very, hidden, i.e. even less obvious than 'not at all obvious'. An understatement is saying something in terms milder than reality; in other words, you're not doing reality justice by describing it in such a mild way.

Thus, to say that 'not at all obvious' is an understatement means that 'not at all obvious' is too mild a term for how not-obvious the algorithm is.

By referring to his comment as the biggest understatement in the book the writer means that in saying that the algorithm is not so obvious he was not really putting it strongly enough. What he now thinks he should have said is something like the algorithm really, really, really isn’t obvious at all. No way. No how. Never in a million years.

You're reading it a bit too literally--the writer is of the opinion to say that that algorithm 'is not at all obvious' is putting it mildly, and suggesting that it is completely out of reach of the observer.